We present an approach to combining three areas of research which we claim are all based on information theory: knowledge representation in Artificial Intelligence and Cognitive Science using prototypes, plans, or schemata; formal semantics in natural language, especially the semantics of the `if-then' conditional construct; and the logic of subjunctive conditionals first developed using a possible worlds semantics by Stalnaker and Lewis. The basic premise of the paper is that both schema-based inference and the semantics of conditionals are based on Dretske's notion of information flow and Barwise and Perry's notion of a constraint in situation semantics. That is, the connection between antecedent $A$ and consequent $B$ of a conditional `if $A$ were the case then $B$ would be the case' is an informational relation holding with respect to a pragmatically determined utterance situation. The bridge between AI and conditional logic is that a prototype or planning schema represents a situation type, and the background assumptions underlying the application of a schema in a situation correspond to channel conditions on the flow of information. Adapting the work of Stalnaker and Lewis, the semantics of conditionals is modeled by a refinement ordering on situations: a conditional `if $A$ then $B$' holds with respect to a situation if all the minimal refinements of the situation that support $A$ also support $B$. We present new logics of situations, information flow, and subjunctive conditionals based on three-valued partial logic that formalizes our approach, and conclude with a discussion of the resulting theory of conditionals, including the "paradoxes" of conditional implication, the difference between truth conditions and assertability conditions for subjunctive conditionals, and the relationship between subjunctive and indicative conditionals.

Extending techniques of Dowd and those of Poizat, we study computational complexity of $r\mathit{TAUT}[A]$ in the case when $A$ is a generic oracle, where $r$ is a positive integer, and $r\mathit{TAUT}[A]$ denotes the collection of all $r$-query tautologies with respect to an oracle $A$. We introduce the notion of ceiling-generic oracles, as a generalization of Dowd's notion of $t$-generic oracles to arbitrary finitely testable arithmetical predicates. We study how existence of ceiling-generic oracles affects behavior of a generic oracle, by which we show that $\{ X: co\mathit{NP}[X] $ is not a subset of $\mathit{NP}[r\mathit{TAUT}[X]]\}$ is comeager in the Cantor space. Moreover, using ceiling-generic oracles, we present an alternative proof of the fact (Dowd) that the class of all $t$-generic oracles has Lebesgue measure zero.

Axioms in set theory typically have the form $\forall z \exists y\forall x(x \in y \leftrightarrow F x z )$, where $F$ is a relation which links $x$ with $z$ in some way. In this paper we introduce a particular linkage relation $L$ and a single axiom based on $L$ from which all the axioms of $\mathrm{Z}$ (Zermelo set theory) can be derived as theorems. The single axiom is presented both in informal and formal versions. This calls for some discussion of pertinent features of formal and informal axiomatic method and some discussion of pertinent features of the system $\mathrm{S}$ of set theory to be erected on the single axiom. $\mathrm{S}$ is shown to be somewhat stronger than $\mathrm{Z}$, but much weaker than $\mathrm{ZF}$ (Zermelo-Fraenkel set theory).

The paper introduces a semantics for the language of propositional additive-multiplicative linear logic. It understands formulas as tasks that are to be accomplished by an agent (machine, robot) working as a slave for its master (user, environment). This semantics can claim to be a formalization of the resource philosophy associated with linear logic when resources are understood as agents accomplishing tasks. I axiomatically define a decidable logic TSKp and prove its soundness and completeness with respect to the task semantics in the following intuitive sense: ${\textbf{TSKp}}\vdash\alpha$ iff $\alpha$ can be accomplished by an agent who has nothing but its intelligence (that is, no physical resources or external sources of information) for accomplishing tasks.